In a large bowl, toss the pieces of chicken in salt, pepper, and cayenne pepper to evenly coat.
In a large skillet over medium heat, add the olive oil and butter.
When hot, add the chicken and cook for 4-5 minutes on each side, or until lightly browned. (Depending on the size of your skillet, you may have to cook the chicken in batches.) Once browned, remove the chicken from the skillet and place it on a plate. The chicken will not be fully cooked at this point. Tent the pieces to keep warm as you make the sauce.
Reduce the heat to medium-low and add the chicken broth, honey, mustard, and lemon juice. Whisk to combine. Bring the mixture to a low simmer, stirring occasionally, scraping the brown bits from the bottom of the pan as you go.
Stir in the heavy cream and sour cream until fully incorporated. Nestle the chicken pieces back into the sauce and simmer for another 5-10 minutes, or until the chicken is cooked through to an internal temperature of 165°F.
While the chicken is cooking, prepare the green beans.
Bring a medium pot of water to a boil. Add green beans and boil for 2-3 minutes.
Drain the green beans and nestle them into the skillet.
Top the dish evenly with the crushed fried onions and serve.